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A172177
Triangle T(n, k) = 1 + abs(n! - k!)*abs(n! - (n-k)!), read by rows.
1
1, 1, 1, 1, 2, 1, 1, 21, 21, 1, 1, 415, 485, 415, 1, 1, 11425, 13453, 13453, 11425, 1, 1, 431401, 499729, 509797, 499729, 431401, 1, 1, 21768481, 24786961, 25250545, 25250545, 24786961, 21768481, 1, 1, 1422454321, 1596592801, 1620622801, 1623767617, 1620622801, 1596592801, 1422454321, 1
OFFSET
0,5
FORMULA
T(n, k) = 1 + abs(n! - k!)*abs(n! - (n-k)!).
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 2, 1;
1, 21, 21, 1;
1, 415, 485, 415, 1;
1, 11425, 13453, 13453, 11425, 1;
1, 431401, 499729, 509797, 499729, 431401, 1;
1, 21768481, 24786961, 25250545, 25250545, 24786961, 21768481, 1;
MATHEMATICA
T[n_, k_]= 1 +Abs[n!-k!]*Abs[n!-(n-k)!];
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
PROG
(Magma)
F:=Factorial; [1 + Abs(F(n)-F(k))*Abs(F(n)-F(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Apr 29 2021
(Sage)
f=factorial; flatten([[1 + abs(f(n)-f(k))*abs(f(n)-f(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 29 2021
CROSSREFS
Sequence in context: A157453 A174174 A156889 * A156725 A141904 A246072
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Jan 28 2010
EXTENSIONS
Edited by G. C. Greubel, Apr 29 2021
STATUS
approved